# Ch 8: Linear Functions

### About This Chapter

## Linear Functions - Chapter Summary

Begin your study of linear functions by learning the slope-intercept form of a linear equation. You can also find out how to use standard form to find intercepts, determine the slope of a line, and differentiate between zero slope and undefined slope.

As you progress through the lessons, instructors show you how to write a linear equation using the point-slope formula or parallel and perpendicular lines' opposite reciprocal. Instructors can also teach you how to compare and contrast two or more linear equations by finding the intersection point on a graph or using the substitution and linear combination methods. You can also learn how to convert systems of equations into matrices and solve equations including linear inequalities.

The chapter concludes with several lessons containing practice questions and examples to show you how these concepts are used to solve real-life problems. Altogether, this chapter is designed to introduce you to the following main topics:

- Slope-intercept and standard form
- Point-slope formula
- Graphing and substitution techniques
- Linear combinations
- Systems of equations
- Linear inequalities

Our experienced instructors make the lesson content approachable and engaging. You can access the video lessons as many times as you'd like in whichever order you need. Use them to review steps in the problem solving process or enhance your understanding of key concepts. When you're ready, there are corresponding self-assessment quizzes you can take to get extra practice solving linear equations.

### 1. What is a Linear Equation?

Most cars won't be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.

### 2. How to Write a Linear Equation

Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if you're given the right information.

### 3. Linear Equations: Intercepts, Standard Form and Graphing

Do you know what to do if an equation doesn't look like y=mx+b?! If not, then this video is for you. Chances are the equation is in standard form, so we'll learn how to use standard form equations, how to graph them and why they can be helpful.

### 4. How to Find and Apply The Slope of a Line

In this lesson, we'll discover all about the slopes of lines. We'll learn about different types of slopes and how to find the slopes of lines. We'll use two methods: the slope formula and the slope-intercept form.

### 5. Graphing Undefined Slope, Zero Slope and More

There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!

### 6. Equation of a Line Using Point-Slope Formula

It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.

### 7. What is a System of Equations?

So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.

### 8. How to Solve Systems of Linear Equations by Graphing

Systems of linear equations are important in many branches of math and science, so knowing how to solve them is important. In this lesson, learn one way to find the solution of a system of linear equations by graphing.

### 9. How to Solve a System of Equations by Substitution

Watch this video lesson to learn how you can solve a system of equations by using the substitution method. Learn the key to using the substitution method and take a quiz to practice your new skills.

### 10. Solving Systems of Equations with Linear Combinations

This lesson will show how to solve Systems of Equations with Linear Combinations. We will use some sample problems and properties to prove the solution is the point of intersection.

### 11. Solving Problems Involving Systems of Equations

Did you ever encounter a problem where you seem to have lots of information, but still have a couple of critical numbers missing? In this lesson, we'll practice solving word problems that require us to set up systems of equations.

### 12. Solving Linear Inequalities: Practice Problems

Linear inequalities may look intimidating, but they're really not much different than linear equations. In this lesson, we'll practice solving a variety of linear inequalities.

### 13. Solving Systems of Equations Using Matrices

Systems of equations appear in all types of real-world applications. A nice way to solve these equations is to use matrix operations like row exchange, multiplication and addition. In this lesson, we show how this is done.

### 14. Using an Inverse Matrix to Solve a System of Linear Equations

This lesson will show you how to solve a system of linear equations by using inverse matrices. Examples and definitions will be provided to help you understand.

### 15. Problem solving using Linear Equations

From sale prices to trip distances, many real life problems can be solved using linear equations. In this lesson, we'll practice translating word problems into linear equations, then solving the problems.

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### Other Chapters

Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course

- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Triangles
- Circles
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards